Delivery of fluids for industrial, chemical and biological applications has evolved to a point where extremely small, or very large, quantities of fluid can be accurately delivered using a variety of pumping and pipetting techniques. In addition, techniques have been developed for eroding surfaces and for applying chemicals to surfaces in very precise quantities and at specific locations. These techniques may be used to apply solutions and suspensions accurately and evenly over a surface to provide consistent surface chemical densities. However, applications may exist where it is not desirable to introduce or deposit solutions or chemicals evenly, but rather as a gradient where the density of an applied material is greater at one part of a surface than it is at another part of the surface.
Traditionally, linear concentration gradients exhibiting a variation in concentration in relation to distance may be formed by allowing solutes to diffuse from a point of high concentration into a material containing the substance at low concentration. After the substance has been allowed to diffuse for a period of time, a concentration gradient may develop extending away from the point source. The fluid may be sampled at various distances from the point source and progressively lower concentrations will generally be detected as the distance from the point source increases. Unfortunately, because materials in solution continue to diffuse to areas of lesser concentration, the concentration of the substance at any one point changes with time, as does the gradient between any two points. It is therefore difficult to proceed with experiments or processes that require a stable gradient. This problem is compounded when steep gradients are required, as steep gradients generally may decay faster than those that are less sloped.
Gradients on surfaces have been produced by methods using self-assembled monolayers (SAMs) including cross-diffusion, photo-immobilization and electrochemical desorption. However, the types of gradients profiles on surfaces that can be produced, the substances that can be used, and the size of the gradients are all limited.
In addition, known fluid gradients may be limited to linear gradients in which concentration decreases or increases by a constant amount over distance. At times, it may be useful to employ gradient that do not increase or decrease linearly, but rather increase, for example, as a squared, cubed or logarithmic function. However, known point source and linear source diffusion techniques are not known to be capable of producing gradients that exhibit these profiles.